MRES 7005 - Fast Imaging Techniques Module 2 Artefacts and Imaging Optimisation for single shot methods Content: Introduction Phase error Phase bandwidth Chemical shift review Chemical shift in pixels Removing chemical shift artefacts Magnetic susceptibility Reducing geometric distortions Receiver bandwith Ramp sampling Fourier regridding Field of view Slew Rate Frequency Encoding Steps 1/36
MRES 7005 - Fast Imaging Techniques Phase encoding steps Segmentation Advantages and Disadvantages of Segmentation Repetition Time (TR) Nyquist or N2 Ghosting (I) Nyquist or N2 Ghosting (II) Nyquist or N2 Ghosting (III) Reduce Nyquist ghosting Recovering SNR and Resolution Summary 2/36
Introduction In Module One, the basic principles FSE and EPI were discussed. When used as single shot methods, a long train of echoes are acquired for a single excitation pulse. As gradients are faster to apply than 180 degree rf pulses, EPI is the faster of the two methods, and has a train of gradient refocussed echoes The oscillating frequency gradient acquires every alternate line in reverse. As a result of the gradient echo train in the EPI readout, the sequence is very susceptible to off resonance effects. Figure 2.1: The traversal of k-space used in EPI. In this module, we shall be discussing the sensitivity of single shot methods to artefacts, particularly EPI. The removal or reduction of these artefacts depends on careful parameter selection and hardware requirements. 3/36
Phase error As already mentioned in Module 1, the longer the echo train length, or the longer the echo spacing, the more signal decay there is between echoes due to T2 in FSE or T2* in EPI. This can result in blurring or lower apparent spatial resolution, due to a filtering of k-space or raw data, called the point spread function. There are added complications when off resonance effects are considered. The magnetic field experienced by an individual nucleus can be altered by off resonance effects, namely: chemical shift magnetic susceptibility. These effects are covered in depth in course MRES7001, Module Seven. The result of these effects is an increase signal decay rate, given by T2*. In all Fourier transform imaging, the lines of k-space are filled using phase encoding gradients to increment the position of k-space; as described in MRES7004. If two components have different frequencies due to chemical shift or susceptibility then they will accumulate additional phase and this will translate to different spatial offsets. In SE, each line of k-space is a separate acquisition, so the phase difference is 'reset' to zero at the beginning of each acquisition. In FSE, the 180o rf pulses within the echo train correct the phase error that builds up. That is, signal decay due to chemical shift and magnetic susceptibility effects is refocused. In EPI, with its gradient echo train, such effects accumulate. The time between adjacent points on the ky axis can be quite long and there is no intervening rf pulse to rephase the MR signal. The long time between adjacent ky points gives rise to a relatively low effective bandwidth in the phase direction. The reconstruction cannot determine whether an increase in phase is legitimate or not. That is, any increase in phase is interpreted in the same manner, whether it arises from phase encoding, or from accumulated phase error. Therefore, off resonance spins that have accumulated phase error are misregistered in the phase encode direction. 4/36
Phase bandwidth Bandwidth is inversely proportional to the sampling time. In the phase direction, the complete range of frequencies over the image in the phase direction becomes: Equation 2.1 where τpe is the time between two successive phase encoding steps, or time between adjacent ky points. The number of pixels by which the phase error is shifted is dependent upon the phase bandwidth per pixel, or BW/Ny. It is the same for the read encoding direction, where the bandwidth per pixel becomes: Equation 2.2 Where t is the sample time, or time between read encoding points. 5/36
Chemical shift review The chemical shift between water and fat is 3.3 ppm. The change in frequency ( ν) generated by this chemical shift can be determined by: Eqn 2.3 where Bσ is δ B0/106. What is ν at 1.5 T? (γ/2π = 42.58 MHz/T) Solution: Bσ = 3.3 1.5/106 = 4.95 10-6 T ν = 42.58 MHz/T 4.95 10-6 T = 210.8 Hz This change in frequency gives rise to a shift in pixels for the chemical that is off resonance. In EPI, this occurs in both the read and phase directions. The chemical shift in pixels is determined by dividing the change in frequency by the bandwidth per pixel. Note that the bandwidth per pixel is equal to BW/Nx (or BW/Ny in the phase direction). What is the chemical shift in pixels for the above example, for a bandwidth along the read direction of 200 khz, with Nx = 128? Solution: Using the same general formula, what is the chemical shift in pixels in the phase direction for the above example? Use a time of 640 µs between phase encoding steps ( τpe) and Ny of 128 in your calculations. Solution: 6/36
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Chemical shift in pixels The total number of pixels in the read direction (nread) and phase direction (nphase) shifted due to the chemical shift tissue difference ( B σ = B0 δ/106) is given by: Eqn 2.4 Eqn 2.5 where t is the sampling time, or time between each read encoding point, τpe is the time between phase encoding points, Nx and Ny are the number of read and phase encoding steps. You can see the derivation of these equations in the Extension screen. Note that Ny τpe in EPI is the time to complete the echo train. In other words, the off resonance frequency shift is proportional to the amount of time the spins are accumulating phase error. Watch the animation below to discover the pixel shifts in the read and phase direction for a variety of different chemical shifts in ppm, and imaging parameters. (Note: SW = sweep width which is similiar to Bandwidth) 8/36
Simulation 2.1: Calculated nphase and nread for different B0, τ peand SW (see on-screen simulation) 9/36
Extension Screen: Derivation of chemical shift in pixels This material is for your information only and is not examinable. To calculate the chemical shift in pixels in the phase direction, the phase bandwidth is used, and the matrix size in the phase direction. 10/36
Removing chemical shift artefacts Fat is shifted a significant amount in the phase direction in EPI images. See Figure 2.2(a) below where the subcutaneous fat has been shifted one-eighth of the FOV. All EPI images are fat suppressed to remove this problem (see Figure 2.2(b)). There are a variety of different fat suppression methods available, and a review can be found in MRES7004, module 8. In Module One, a comparison was made between a SE, FSE and EPI image of the brain (Figure 2.3). The missing element was fat, because it had been successfully suppressed. This is why the contrast of SE-EPI or GE-EPI resembles a fat suppressed SE or GE image respectively. (a) 11/36
(b)figure 2.2: (a) Non fat suppressed and (b) fat suppressed EPI of brain. Figure 2.3: (a) Spin echo, (b) fast spin echo, and (c) EPI images of the brain (Source: Reproduced by courtesy of GE Medical Systems (1995) Echo Planar Imaging: Principles and Applications, p. 12.) 12/36
Magnetic susceptibility Adjacent tissues with different magnetic susceptibilities cause disruptions to the local field (see Module 7, MRES7001, Susceptibilities). Some examples of this are bone-tissue interfaces found in the cancellous or 'spongy' bone, or the air-tissue interfaces found in the lung and in the sinuses, such as the ethmoid, maxillary, and mastoid sinuses. Any water protons within this local field inhomogeneity will precess off resonance. The frequency shift of these spins will vary from region to region and patient to patient, but will behave the same as off resonance fat. That is, they are wrongly positioned in the phase encoding direction. Note that very large inhomogeneity in the local field, like those caused by metal braces on the teeth, are still going to cause large distortions even with the most perfectly optimised sequence. Obviously suppressing the water signal as well as fat defeats the purpose. Figure 2.4: A single shot EPI image of the brain with an 256 echoes in the train. The time between each image was 2.7 ms, giving a total train length time of 700 ms. Source: Reproduced by courtesy of GE Medical Systems (1996) EPI Applications Guide, p. 9. 13/36
Reducing geometric distortions One way to reduce the impact of the geometric distortion is to swap the phase and read directions.it is possible to minimise the impact by placing the phase direction along a natural axis of symmetry (see figure 2.5) (a) (b) Figure 2.5: Two images of the brain are shown, identical in imaging parameters except for the placement of the phase encoding direction. The phase lies from right to left in (a) and anterior to posterior in (b) 14/36
Figure 2.6 To reduce the degree of distortion the echo train length or echo spacing needs to be reduced. The longer the ETL, the more time the spins have to accumulate phase error and the greater the distortions. For FSE, a shorter the echo spacing (or ESP) means the less blurring occurs within the image. In EPI, reducing the echo spacing also decreases the blurring, but, more importantly, also decreases the geometric distortion. Figure 2.6: The read encoding gradient and the sampling time during usual gradient performance (no ramp sampling). There are several methods to reduce the echo spacing. Unfortunately, as with most things in EPI, if one parameter is changed, another aspect is also changed, be it signal to noise, spatial resolution, or scan time (see Table 2.1). Parameter Echo Spacing Slew Rate Receiver Bandwidth Echo Train Length Signal to Spatial Noiseratio Resolution Scan Time _ Geometric Distortion Frequency Encoding Steps Phase Encoding Steps _ Frequency FOV _ Phase FOV _ _ Ramp Sampling _ Field Strength _ Table 2.1: Relationship between parameters in EPI and technical and image components 15/36
Receiver bandwidth The rf receiver bandwidth describes how fast the MR signal can be digitised. The higher the receiver bandwidth (RBW) the faster the digitisation can occur. Receiver bandwidth = 1/ t (Eqn 2.6) where t is the time between samples, or the dwell time (see Figure 2.6). Figure 2.7: Data acquisition during a simplified trapezoidal gradient waveform. RBW determines the range of frequencies that will be sampled by the analogue digital converter (ADC), spatially encoded by the frequency or readout gradient. To have enough image data to create and display an image, a balance must be found between the range sampled and the time needed to sample them. For example, to avoid wrap around artefact the receiver must obey the following condition: RBW = γ Gx FOV (Eqn 2.7) 16/36
Figure 2.8: The relationship between receiver bandwidth and frequency gradient If the RBW is increased, the amount of time at the flat top of the gradient reduces significantly. (see Figure 2.8) Shortening the duration of the flat top reduces ESP and geometric distortion. However, as RBW increases, more inherent noise is sampled along with the signal, decreasing the signal to noise ratio. Eqn 2.8 17/36
Ramp Sampling In a trapezoid gradient waveform, the sampling of spins usually occurs during the application of a constant gradient (the 'flat' portion) (Figure 2.9a). The time duration of the flat top is dependent on the frequency encoding matrix and the dwell time. It is possible to collect or sample the echo while the gradient is rising and falling (ramping in either positive or negative direction), as well as the flat top. This is referred to as ramp sampling (Figure 2.9b). Figure 2.9 (Left): Comparing normal data acquisition (a) with ramp sampling (b). Ramp sampling can be used either to maintain the current spatial resolution while decreasing the echo spacing (Figure 2.10 a), or it can be used to increase the resolution while maintaining the same echo spacing (Figure 2.10 b). Figure 2.10 (Right): Gradient waveforms where ESP is reduced (a) or spatial resolution is increased (b). 18/36
Spins being sampled during the ramp experience a non-constant gradient and therefore have different encoding values. The changing value of the magnetic field under the ramp is predictable and consistent, and the data must be repositioned or regridded within k-space before Fourier Transform (see see Extension screen). 19/36
Extension Screen: Fourier Regridding Fourier Transform can only occur on k-space data that are linearly spaced along a two-dimensional grid. The position in k-space is determined by: The data points sampled under a ramping gradient experience a nonlinear gradient field. To make sure that k is the same for all points they must be sampled at different times. This requires a variable bandwidth filter to minimise noise. Using a variable bandwidth can lead to reduced signal to noise. Alternatively, it is possible to over-sample in k-space by defining a sample rate based upon the maximum gradient: The Nyquist criteria is satisfied by this sampling rate. The resulting data will still not be uniformly spaced in k-space as the gradient varies with time and the data should be interpolated before reconstruction. The change in gradient field is a known quantity and the raw data can be corrected by convolution with an apodised sinc kernal. This approach is useful if the available hardware is not flexible enough to implement non-uniform sampling times, but the method does require more data storage and processing. Note that the raw data in k-space generated by EPI has to be reordered anyway prior to Fourier transform. Each second line which is encoded from right to left would have to be temporally reversed (back into left to right orientation) prior to reconstruction. 20/36
Field of view The field of view (FOV) is proportional to the sampling rate ( t) and gradient strength (Gread): Eqn 2.9 Or in other words, it is inversely proportional to the area under the gradient t Gread frequency encoding matrix). Usually the field of view would be determined by the size of the area of interest. The geometric distortion in EPI is a percentage of the field of view. For example, a geometric distortion that is 10% of the FOV appears less with a 20 cm FOV in the phase encoding direction than with a 40 cm FOV (Figure 2.11). However, the Nyquist ghost is also shifted half the FOV away, and will overlap less with the original image where the larger FOV is in the phase encoding direction. Figure 2.11: (a) 20 cm FOV, (b) 40 cm FOV. In the frequency direction, larger than optimal fields of view might be necessary to reduce geometric distortions. The amplitude of the frequency gradient must increase to obtain smaller field of views. However, for a fixed slew rate, the rise time required will increase as the gradient amplitude increases. This translates to an increased ESP (given that all other parameters remain the same) (Figure 2.12). 21/36
Figure 2.12: FOV and gradient shape As for conventional sequences, decreasing FOV results in a loss in signal to noise. Signal to noise is directly proportional to the field of view (SNR approximately equals to FOV) 22/36
Slew Rate To make the most of smaller fields of view or thinner slices, the slew rate of the gradient must be able to increase. The gradient slew rate is the rate of ascent to reach the gradient amplitude, or gradient amplitude divided by the rise time. In Figure 2.13, gradient A with the faster slew rate has a shorter ESP and therefore will result in a higher quality image with less geometric distortions. The required time to play out all the gradients will take less time for A resulting in a faster image acquisition, or shorter ETL, or time to acquire more slices during TR. Note that all other parameters, such as signal to noise and resolution, remain the same. Figure 2.13: Gradients A and B, both with the same amplitude but different slew rates. 23/36
Frequency Encoding Steps The larger the frequency matrix, the higher the resolution in the frequency direction. The frequency matrix size (Nx) is related to the pixel dimension in the frequency direction ( x) and the field of view by the following: Eqn 2.10 Increasing the number of frequency encoding steps increases the gradient duration and increases ESP (Figure 2.14). It is quite common for EPI images acquired on conventional MR systems to have medium-to-low resolution matrices (from 32 up to 128) due to ESP constraints. To prevent unacceptable increases in geometric distortion, increases in frequency steps should be balanced with increases in receiver bandwidth. Alternatively, the EPI image can be acquired in a number of segments, or over several repetition times instead of acquiring the whole image in a single shot. This is known as multi-shot or segmented EPI and requires a new excitation pulse or TR per segment (see later Screen). Figure 2.14: Interaction between Nx and gradient shape 24/36
Phase Encoding Steps Increasing the number of phase encoding steps increases the echo train length in single shot FSE and EPI. The echo spacing does not change, but blurring will increase depending upon the T2 /T2* time of the tissue of interest. In the case of EPI, there is also more time for phase errors to accumulate, giving rise to greater geometric distortion. Increasing the number of phase encoding steps does not directly increase the scan time, providing the slice coverage is maintained. The overall time to acquire the image is increased, but this is only a portion of the 'dead time' or recovery time (see Figure 2.15). The remainder is usually devoted to slice acquisition. Only if TR needs to be increased to maintain the slice coverage does the scan time increase. One way of increasing the resolution without increasing the frequency of phase encoding steps is known as zero filling. For example, a 96 x 96 matrix can be acquired and then interpolated to a 256 x 256 image. The other way of improving the resolution without image blurring or distortion is segmenting to a multi-echo method rather than single shot, parallel imaging, or using the symmetry of k-space (these last two will be discussed in later modules). Figure 2.15: Schematic of acquisition time 25/36
Segmentation In a multi-shot FSE or EPI method, several excitation pulses are needed to collect the whole of k-space. Eqn 2.11 The degree of segmentation can be referred to either as the echo train length per excitation or the complete number of 'shots' used to acquire the full image. For example, 256 phase encoding steps acquired in 32 shots would have an echo train length of 8. Segmentation commonly occurs in an interleaved manner, where the extent of k-space is covered (e.g. -kx(max) to +kx(max)), but in reduced detail. Animation 2.2: Interleaved segmentation of a segmented EPI sequence See animation on screen 26/36
Advantages and Disadvantages of Segmentation Segmentation provides a number of advantages and disavantages. Segmentation places less stress on the gradients compared with single shot methods, particularly EPI. Phase errors have less time to build up compared with single shot EPI, thus reducing the magnetic susceptibility artefacts (see Figure 2.16). Less blurring occurs in FSE methods as the echo train length reduces. Segmented methods allow for increased resolution without losing image quality. Segmentation allows for T1 weighting to be introduced Segmented methods take longer to perform. The scan time is equal to TR x Ns x NA. Because of the above, segmented methods can be more prone to motion artefacts than single-shot. Segmentation methods are prone to specific artefacts, because of the complex coverage of k-space. EPI is more susceptible to this compared to FSE due to the alternating directions in k-space (L-R then R-L). 27/36
Figure 2.16: Demonstration of the reduction of geometric distortion as the number of shots is increased. (a) 2 shots (ETL 128) (b) 4 shots (ETL 64) (c) 8 shots (ETL 32) (d) 16 shots (ETL 16). 28/36
Repetition Time (TR) As there is only one TR in single shot methods, the effective TR is infinite, and is only used to determined the space of time allocated for multi-slice selection. In segmented or multi-shot versions of EPI and FSE, the lines of k-space are being filled over several TR periods. In this case, the TR should be selected according to the desired contrast. The longer the repetition time, the less T1 -weighting there is within the image, but the higher the SNR. In multi-shot EPI or FSE, if the TR is shorter than the 5T1 of the tissue, the longitudinal magnetisation will be slowly decreasing with each new excitation. This also occurs for single-shot methods where you are repeatedly exciting the same slices over time (ie following a temporal series of events). Eventually, the spins become saturated and reach steady-state magnetisation. This is where the amount of magnetisation flipped into the transverse plane can fully recovery within the TR. To avoid artefacts, the first few segments with changing SNR are ignored - usually additional excitation pulses are applied but the information discarded. Figure 2.18: Diagram illustrating steady state magnetisation. 29/36
Nyquist or N/2 Ghosting (I) Time varying magnetic field gradients result in current induction (eddy currents) in the various conductive components of the rest of the imaging instrument. These, in turn, create magnetic field gradients that may persist after the primary gradients are switched off. While a problem in conventional imaging, they are more severe in EPI. The gradient amplitudes and switching rates in EPI are usually much greater, causing larger eddy currents. Also, the long readout period in EPI results in more opportunity for image distortion from eddy currents. Eddy currents (plus gradient power supply and pre-emphasis problems) transform the trapezoid gradient shape from the idealised version shown so far into a non-linear shape (Figure 2.18). Since the transformation is unknown it cannot be accounted before during acquisition. K-space lines corresponding to positive and negative oscillating gradients are shifted. Figure 2.18: The results of eddy currents on gradient waveforms and in k -space. 30/36
Nyquist or N/2 Ghosting (II) The Fourier transform of two shifted signals in k-space, superimposed, has an interferogram effect, as seen in Figure 2.19. There is a ghost one-half the field of view away in the phase encoding direction. This is referred to as a Nyquist or N/2 ghost. The modulation of the ghost is 180o out of phase relative to the original, which can lead to interference patterns when the images overlap (black lines). Figure 2.19: Examples of the N/2 ghost artefact in EPI. From left to right the degree of shift ( ) is getting smaller. However, when a segmented EPI method is used, the ghosting is increased. Where there was one ghost shifted half the FOV from the original image, there would now be the same number of ghosts as there are number of shots (Ns) in the phase direction. They would be separated by: 31/36
Nyquist or N2 Ghosting (III) That is, the spacing between ghosts in segmented EPI are smaller than for single shot EPI, and they are more likely to overlap the original image. See Figure 2.20b a) Figure 2.20: Four shot EPI method showing the shifts in k-space (a) and the resulting ghosting (b). 32/36
Reduce Nyquist ghosting To reduce N/2 ghosting: use appropriately designed coils to minimise eddy current induction (see MRES7002, Module Five) adjust the sampling clock in the hardware to make sure the timing between signal digitisation and gradient activity is calibrated within the software, add an extra timing factor to incorporate an appropriate phase shift in theraw data use the shift parameter ( from Figure 2.18) during reconstruction to construct an artefact free image. In single shot it is possible to calculate a phase shift parameter from regions where the original and the ghosts have not overlapped and use this to reconstruct an artifact free image. This is not possible with interleaved experiments, in which the overlapping of ghosts is almost unavoidable. The solution is to perform a reference or calibration scan without phase gradients to measure the phase shift. From the raw data, phase correction values can be derived. 33/36
Recovering SNR and Resolution In trying to decrease the geometric distortion through parameter optimisation, signal to noise is often sacrificed. Keep in mind that different parameters will affect SNR to different extents. There are several ways of recovering SNR: using receiver coils to improve signal to noise increase slice thickness (lose resolution in the slice direction) signal averaging (which increases overall scan time) increase the number of segments change the EPI mode to SE-EPI - this has slightly less dependence upon T2* use magnets with large field strengths. The SNR increases with increasing field strength, but chemical shift and geometric distortions also increase. Resolution is the other area where sacrifices are made, particularly in EPI. Resolution depends upon the maximum gradient amplitude available and the sampling time. To increase resolution: increase gradient amplitude The best resolution is achieved by using the maximum possible gradient amplitude. increase gradient duration...but suffer more geometric distortions use a segmented or multi-shot method Use parallel imaging (see Module 6) Undersample k-space but reconstruct at a higher resolution (zero filling; k-space symmetry; interpolation) 34/36
Summary Artefact Image Blurring Chemical Shift Artefact Chemical Shift Artefact Nyquist Ghosting To remove or reduce Reduce ESP Fat Suppression/Saturation Phase encoding along natural axis of symmetry Reduce ETL Reduce ESP Gradient Shielding Adjust sampling clock Apply a phase shift in software; calculated from a reference scan. Reducing Echo Spacing Imaging Parameter Receiver bandwidth Ramp Sampling FOV - frequency direction Slew rate Ny - phase matrix Nx - frequency matrix Effect Large bandwidths mean less distortions but more noise. Use to decrease distortions or improve resolution, but regridding is necessary Increasing will lower geometric distortions if your slew rate is fixed. Faster slew rate means shorter ESP and ETL, less image blurring and less distortions. Increasing will increase resolution, but increase echo train length. Increasing will increase resolution, but increase distortion Review Questions What causes image blurring in single shot sequences? How can blurring be removed or reduced and what impact does that have? What is a chemical shift artefact? Which sequence is most affected by it and why? How can chemical shift artefact be removed or reduced and what impact does that have? What is Nyquist ghosting? Which sequence is most affected by it and why? 35/36
How can Nyquist ghosting be removed or reduced and what impact does that have? What is geometric distortion? Which sequence is most affected by it and why? How can geometric distortion be removed or reduced, and what impact does that have? 36/36